Question

find the area of the figure. round to the nearest tenth, if necessary. 32 mm 40 mm mm²

Explanation:

Step1: Identify component shapes

The figure is composed of a rectangle, a parallelogram and a trapezoid. The rectangle has length $l = 40$ mm and width $w = 32$ mm. The parallelogram has base $b = 40$ mm and height $h = 32$ mm. The trapezoid has bases $b_1=32$ mm and $b_2 = 2\times32=64$ mm and height $h = 40$ mm.

Step2: Calculate area of rectangle

The area formula for a rectangle is $A_{rect}=l\times w$. So $A_{rect}=40\times32 = 1280$ $mm^{2}$.

Step3: Calculate area of parallelogram

The area formula for a parallelogram is $A_{par}=b\times h$. So $A_{par}=40\times32=1280$ $mm^{2}$.

Step4: Calculate area of trapezoid

The area formula for a trapezoid is $A_{trap}=\frac{(b_1 + b_2)h}{2}$. Substitute $b_1 = 32$ mm, $b_2=64$ mm and $h = 40$ mm. Then $A_{trap}=\frac{(32 + 64)\times40}{2}=\frac{96\times40}{2}=1920$ $mm^{2}$.

Step5: Calculate total area

$A = A_{rect}+A_{par}+A_{trap}=1280+1280 + 1920=4480$ $mm^{2}$.

Answer:

$4480$